Scilab Function
Last update : April 1993

remezb - Minimax approximation of magnitude response

### Calling Sequence

  `[an]=remezb(nc,fg,ds,wt)`

### Parameters

- `nc`: Number of cosine functions
- `fg`: Grid of frequency points in [0,.5)
- `ds`: Desired magnitude on grid `fg`
- `wt`: Weighting function on error on grid `fg`
- `an`: Cosine filter coefficients

### Description

Minimax approximation of a frequency domain magnitude response. The approximation takes the form `h = sum[a(n)*cos(wn)]` for n=0,1,...,nc. An FIR, linear-phase filter can be obtained from the the output of the function by using the following commands

             hn(1:nc-1)=an(nc:-1:2)/2;
             hn(nc)=an(1);
             hn(nc+1:2*nc-1)=an(2:nc)/2;

### Examples

    // Choose the number of cosine functions and create a dense grid
    // in [0,.24) and [.26,.5)
    nc=21;ngrid=nc*16;
    fg=.24*(0:ngrid/2-1)/(ngrid/2-1);
    fg(ngrid/2+1:ngrid)=fg(1:ngrid/2)+.26*ones(1:ngrid/2);
    // Specify a low pass filter magnitude for the desired response
    ds(1:ngrid/2)=ones(1:ngrid/2);
    ds(ngrid/2+1:ngrid)=zeros(1:ngrid/2);
    // Specify a uniform weighting function
    wt=ones(fg);
    // Run remezb
    an=remezb(nc,fg,ds,wt)
    // Make a linear phase FIR filter
    hn(1:nc-1)=an(nc:-1:2)/2;
    hn(nc)=an(1);
    hn(nc+1:2*nc-1)=an(2:nc)/2;
    // Plot the filter's magnitude response
    plot(.5*(0:255)/256,frmag(hn,256));
    //////////////
    // Choose the number of cosine functions and create a dense grid in [0,.5)
    nc=21; ngrid=nc*16;
    fg=.5*(0:(ngrid-1))/ngrid;
    // Specify a triangular shaped magnitude for the desired response
    ds(1:ngrid/2)=(0:ngrid/2-1)/(ngrid/2-1);
    ds(ngrid/2+1:ngrid)=ds(ngrid/2:-1:1);
    // Specify a uniform weighting function
    wt=ones(fg);
    // Run remezb
    an=remezb(nc,fg,ds,wt)
    // Make a linear phase FIR filter
    hn(1:nc-1)=an(nc:-1:2)/2;
    hn(nc)=an(1);
    hn(nc+1:2*nc-1)=an(2:nc)/2;
    // Plot the filter's magnitude response
    plot(.5*(0:255)/256,frmag(hn,256));

### See Also

`eqfir`,

### Author

C. B.